Benenti tensors: a useful tool in projective differential geometry

DOI10.1515/coma-2018-0006zbMath1397.53027OpenAlexW2804853009WikidataQ114053142 ScholiaQ114053142MaRDI QIDQ720768

Gianni Manno, Andreas Vollmer

Publication date: 18 July 2018

Published in: Complex Manifolds (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/coma-2018-0006

zbMATH Keywords

projectively equivalent metricsprojective connectionsBenetti tensorsLevi-Civita metrics

Mathematics Subject Classification ID

Projective differential geometry (53A20) Projective connections (53B10)

Related Items (4)

3-dimensional Levi-Civita metrics with projective vector fields ⋮ Projectively equivalent 2-dimensional superintegrable systems with projective symmetries ⋮ Normal forms of two-dimensional metrics admitting exactly one essential projective vector field ⋮ (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-dimensional metrics admitting precisely one projective vector field
• On the transformations of the dynamical equations. With an appendix by Sergio Benenti.
• Geodesically equivalent metrics in general relativity
• Separability in Riemannian manifolds
• Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two
• Geometrical interpretation of Benenti systems
• Geodesic equivalence via integrability
• Bihamiltonian structures and Stäckel separability
• Metrisability of two-dimensional projective structures
• A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
• Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
• Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics
• On the geometry of Grassmannian equivalent connections
• Bi-differential calculi and bi-Hamiltonian systems
• Metric connections in projective differential geometry

This page was built for publication: Benenti tensors: a useful tool in projective differential geometry